Confrey says that "These misconceptions appear to be resistant to traditional forms of instruction." Is she referring to the specific misconceptions in the cited work, or the more broad category of what she calls "severe student misconceptions"? (JMG)
On page 108 last full paragraph, the language of '..denial of direct and assured access to "the way things really are"...' and goes on to say that that constructivists "reject any claim which entails the correspondence of an idea with an objective reality." Does the wording seems to favor one epistemological classification over the other or does it seem fairly neutral? (JMG)(JLK)
(Extending the previous question) - Given Confrey's (and then Simon's) account of constructivism, does this suggest that constructivism first developed primarily towards what we now refer to as 'radical' and 'social' constructivism? If so, how and when did the weaker forms of constructivism develop? (JLK)
Confrey asserts personal autonomy is "the backbone of the process of construction" (p. 111) and provides other characterizations of "powerful constructions." Would social constructivists agree? What are other qualities of powerful constructions might we extend on p. 111-112? (AJ)
Simon (1995, Reconstructing...)
What is symbolic interactionism (p116)? The author seems to be using it synonymously with a sociocultural orientation as the difference between radical constructivism and social constructivism, but it's used separately from the sociocultural piece, which seems to imply that it is not quite the same thing. Also there is implied that social constructivism is not purely psychological, but sits at the intersection of psychology and sociology; in that perspective is a comparison between the purely psychological radical constructivism and the (in this case stated as) hybrid theory of social constructivism an apples to oranges type of comparison? (JMG)
On page 119-120 there is a discussion about students first discovering how to solve contextual problems, then being shifted in their focus to the broader implications of the root concept; is this a good example of what Confrey, and the prior weeks readings, refer to as a shift from week construction to strong construction? (JMG)
Simon reports (p. 138) that the intended duration of the rectangles problem was one to two days, but he chose to allow additional development, lasting a total of eight days (and arguably allowed for deeper and broader student thinking and learning). What are some of the possible critiques that other researchers might have on this? Would something like this be allowable or beneficial in an elementary classroom? (JLK)
The Mathematics Teaching Cycle described on p. 141 provides four themes (student thinking, evolving knowledge, instructional planning, and continual change in teacher's hypothetical learning trajectory). How large-scale is this notion of teachers using this model, specifically in relation to the fourth theme: "the continually changing knowledge of the teacher creates continual change in the teacher's hypothetical learning trajectory?" (AJ)
Steffe & D'Ambrosio
When the authors talk about creating a unit of units of units, is it the same thing as talking about encapsulation/reification? (JMG)
How does the description of the notion of Zone of Potential Construction compare to and deviate from Vygotsky's Zone of Proximal Development and Simon's Hypothetical Learning Trajectory? (JLK)
Do Steffe & D'Ambrosio seem to be more in favor of Simon's framework, generally opposed to it, or half-way between the two? What evidence supports (y)our thinking? (JLK)
Simon (1995, response to Steffe & D'Ambrosio)
In this response, Simon seeks to discuss a "significant, although not major, point of disagreement" to Steffe & D'Ambrosio's article. Does SImon distinguish the difference between significant and major, and is his argument consistent with his claim? (JLK)
Steffe & D'Ambrosio and Simon seem to place different emphasis on social processes in their models (similar to those of radical vs social constructivism). What are the classroom practice implications of this, and how does it reflect in differences among describing student learning? (AJ)
Simon, Tzur, Heinz & Kinzel (2004)
How does this article reflect the (1995) discourse between Simon and Steffe & D'Ambrosio?
What does the example of Micki's work and thinking add to the discussion of constructivism? How does this experiment connect to (and build on) Piaget's experiments and interviews?
Across the readings
What do we think are the most critical implications for the work of teachers, with respect to constructivist views and frameworks? (JLK)
Given the consistent implication that constructivist views do not lead to a single model (or a confined set of models) for instruction and learning, what are some of the practical pedagogical issues one could predict and should anticipate? (JLK)
Looking back (15 + years after almost all of these readings), how might we connect recent trends in textbook adoption and instruction to the influence of constructivist ideas?
What are the similarities and differences among the tenets of the different teaching models and what implications does this have on classroom practice? (AJ)
NOTES FROM IN-CLASS 2/13/12 NOTES FROM IN-CLASS 2/13/12 NOTES FROM IN-CLASS 2/13/12
Confrey (1990)
What constructivism implies for instruction
Criticizes direct instruction
Set of assumptions for constructivist teaching model(s)
pg 107 - 3 assumptions for direct instruction.
Makes sense from a timeline
"Less-developed" than Simon and Steffe discourse in 1995
Alternative set of assumptions (p 112)
1) Teachers must build models of students constructions - personal case histories
2) Radical Constructivist perspective - interactive process
3) The STUDENT must decide in the adequacy of his/her own constructions (we might not be able to know students' constructions). Student autonomy is a key focus. "backbone of the process of construction"
Simon (1995)
Social-constructivist orientation
Asserts that constructivism does not dictate
The idea of area with multiplication
Different revisions of the problems/tasks based on information gathered on students' thinking
Area of the blob as an extension task
Cognitive conflict, perturbation, disequilibrium
Hypothetical Learning Trajectory (HLT). (p. 136)
1) Teacher-centered HLT
2) New goals based on what was learned (cyclical)
Why is this a constructivist model (Q posed by Dr. Kim)?
A: The teacher's constructive processes, the HLT is an iterative, construction-based model for thinking about crafting instruction.
Steffe & D'Ambrosio's reaction to Simon
There is a kind of teaching that can be called constructivism
They strengthen the implications for teaching
Quite supportive of Simon's idea
Slight modifications/suggestions for the research reported by Simon
"producing a unit of units of units" - implications for reification, encapsulation, reflective abstraction?
Comments on HLT. Things seem to fit
Introduce Zone of Potential Construction. p. 154
This ZPC may fit into Simon's model for the Teaching Cycle (Simon, pg 137). In other words, the ZPC builds on and refines Simon's Teaching Cycle.
Simon's reaction to Steffe & D'Ambrosio
Simon is still careful to avoid the implication that there is one kind of constructivist teaching.
Disagreement about "activating prior knowledge" (p. 161) Simon thought that just seeing prior knowledge is not sufficient - teacher should see the students navigate perturbations. Steffe & D'Ambrosio emphasized the role of activating prior knowledge.
- Confrey says that "These misconceptions appear to be resistant to traditional forms of instruction." Is she referring to the specific misconceptions in the cited work, or the more broad category of what she calls "severe student misconceptions"? (JMG)
- On page 108 last full paragraph, the language of '..denial of direct and assured access to "the way things really are"...' and goes on to say that that constructivists "reject any claim which entails the correspondence of an idea with an objective reality." Does the wording seems to favor one epistemological classification over the other or does it seem fairly neutral? (JMG)(JLK)
- (Extending the previous question) - Given Confrey's (and then Simon's) account of constructivism, does this suggest that constructivism first developed primarily towards what we now refer to as 'radical' and 'social' constructivism? If so, how and when did the weaker forms of constructivism develop? (JLK)
- Confrey asserts personal autonomy is "the backbone of the process of construction" (p. 111) and provides other characterizations of "powerful constructions." Would social constructivists agree? What are other qualities of powerful constructions might we extend on p. 111-112? (AJ)
Simon (1995, Reconstructing...)- What is symbolic interactionism (p116)? The author seems to be using it synonymously with a sociocultural orientation as the difference between radical constructivism and social constructivism, but it's used separately from the sociocultural piece, which seems to imply that it is not quite the same thing. Also there is implied that social constructivism is not purely psychological, but sits at the intersection of psychology and sociology; in that perspective is a comparison between the purely psychological radical constructivism and the (in this case stated as) hybrid theory of social constructivism an apples to oranges type of comparison? (JMG)
- On page 119-120 there is a discussion about students first discovering how to solve contextual problems, then being shifted in their focus to the broader implications of the root concept; is this a good example of what Confrey, and the prior weeks readings, refer to as a shift from week construction to strong construction? (JMG)
- Simon reports (p. 138) that the intended duration of the rectangles problem was one to two days, but he chose to allow additional development, lasting a total of eight days (and arguably allowed for deeper and broader student thinking and learning). What are some of the possible critiques that other researchers might have on this? Would something like this be allowable or beneficial in an elementary classroom? (JLK)
- The Mathematics Teaching Cycle described on p. 141 provides four themes (student thinking, evolving knowledge, instructional planning, and continual change in teacher's hypothetical learning trajectory). How large-scale is this notion of teachers using this model, specifically in relation to the fourth theme: "the continually changing knowledge of the teacher creates continual change in the teacher's hypothetical learning trajectory?" (AJ)
Steffe & D'Ambrosio- When the authors talk about creating a unit of units of units, is it the same thing as talking about encapsulation/reification? (JMG)
- How does the description of the notion of Zone of Potential Construction compare to and deviate from Vygotsky's Zone of Proximal Development and Simon's Hypothetical Learning Trajectory? (JLK)
- Do Steffe & D'Ambrosio seem to be more in favor of Simon's framework, generally opposed to it, or half-way between the two? What evidence supports (y)our thinking? (JLK)
Simon (1995, response to Steffe & D'Ambrosio)- In this response, Simon seeks to discuss a "significant, although not major, point of disagreement" to Steffe & D'Ambrosio's article. Does SImon distinguish the difference between significant and major, and is his argument consistent with his claim? (JLK)
- Steffe & D'Ambrosio and Simon seem to place different emphasis on social processes in their models (similar to those of radical vs social constructivism). What are the classroom practice implications of this, and how does it reflect in differences among describing student learning? (AJ)
Simon, Tzur, Heinz & Kinzel (2004)Across the readings
NOTES FROM IN-CLASS 2/13/12 NOTES FROM IN-CLASS 2/13/12 NOTES FROM IN-CLASS 2/13/12
Confrey (1990)
Simon (1995)
Steffe & D'Ambrosio's reaction to Simon
Simon's reaction to Steffe & D'Ambrosio